3D Modelling of Electrical Discharges

Abstract

Long electrical discharge patterns in 3D were simulated using a stochastic dielectric breakdown model. The 2D stochastic model introduced by the Niemeyer et al. was modified to simulate the electrical breakdowns in 3D. To compare and classify the simulated breakdown patterns, fractal techniques were used. The simulated electrical breakdown patterns dependent highly on η , the exponent of the cell potentials defined in the breakdown probability equation. For small η values (η ≈ 2), highly complex discharge patterns with many branches having fractal dimension of 1.66 ± 0.02 was observed. When η increases (η ≈ 10), the growth patterns effectively loose their fractal structure and become a curve with dimension 1. In each 3D simulated pattern, 2D vertical projections on XZ plane and YZ plane were analyzed. By studying the fractal dimension of the projections, most suitable η value for simulating discharge patterns can be deduced. 1.